While deep-learning models have demonstrated skillful El Ni\~no Southern Oscillation (ENSO) forecasts up to one year in advance, they are predominantly trained on climate model simulations that provide thousands of years of training data at the expense of introducing climate model biases. Simpler Linear Inverse Models (LIMs) trained on the much shorter observational record also make skillful ENSO predictions but do not capture predictable nonlinear processes. This motivates a hybrid approach, combining the LIMs modest data needs with a deep-learning non-Markovian correction of the LIM. For O(100 yr) datasets, our resulting Hybrid model is more skillful than the LIM while also exceeding the skill of a full deep-learning model. Additionally, while the most predictable ENSO events are still identified in advance by the LIM, they are better predicted by the Hybrid model, especially in the western tropical Pacific for leads beyond about 9 months, by capturing the subsequent asymmetric (warm versus cold phases) evolution of ENSO.

We introduce an interpretable-by-design method, optimized model-analog, that integrates deep learning with model-analog forecasting, a straightforward yet effective approach that generates forecasts from similar initial climate states in a repository of model simulations. This hybrid framework employs a convolutional neural network to estimate state-dependent weights to identify initial analog states that lead to shadowing target trajectories. The advantage of our method lies in its inherent interpretability, offering insights into initial-error-sensitive regions through estimated weights and the ability to trace the physically-based evolution of the system through analog forecasting. We evaluate our approach using the Community Earth System Model Version 2 Large Ensemble to forecast the El Ni\~no-Southern Oscillation (ENSO) on a seasonal-to-annual time scale. Results show a 10% improvement in forecasting equatorial Pacific sea surface temperature anomalies at 9-12 months leads compared to the original (unweighted) model-analog technique. Furthermore, our model demonstrates improvements in boreal winter and spring initialization when evaluated against a reanalysis dataset. Our approach reveals state-dependent regional sensitivity linked to various seasonally varying physical processes, including the Pacific Meridional Modes, equatorial recharge oscillator, and stochastic wind forcing. Additionally, disparities emerge in the sensitivity associated with El Ni\~no versus La Ni\~na events. El Ni\~no forecasts are more sensitive to initial uncertainty in tropical Pacific sea surface temperatures, while La Ni\~na forecasts are more sensitive to initial uncertainty in tropical Pacific zonal wind stress. This approach has broad implications for forecasting diverse climate phenomena, including regional temperature and precipitation, which are challenging for the original model-analog approach.

The El Niño-Southern Oscillation (ENSO), characterized by anomalous sea surface temperature (SST) in the tropical Pacific, exhibits notable diversity in its temporal evolution and spatial distribution of anomalies. The El Niño events of 1982-83 and 1997-98, for instance, recorded exceptionally high sea surface temperature anomaly (SSTA) values in the eastern equatorial Pacific, whereas the El Niño of 2002-03 were notably less extreme and primarily restricted to the central equatorial Pacific (McPhaden, 2004). Despite each being categorized as an El Niño, the 2002-03 event exhibited global climate conditions distinct from those of the earlier two events. In order to describe these event-to-event differences, El Niño events have been categorized as Eastern Pacific (EP), and Central Pacific (CP) types (Capotondi et al., 2020). EP El Niño events typically have their peak SSTA in the Eastern Pacific, exhibit stronger intensities, and a largely reduced zonal thermocline slope, resulting in the discharge of warm water from the equatorial thermocline. In contrast, CP events show peak SSTA in the Central Pacific and are comparatively weaker with more limited changes in zonal thermocline slope and reduced warm water discharge (Kug, Jin, and An, 2009; Capotondi, 2013). Despite considerable research, the underlying causes of ENSO diversity remain elusive (Lee and McPhaden, 2010; Capotondi et al., 2015; Capotondi et al., 2020). And while some general circulation models (GCMs) do exhibit ENSO event-to-event differences, their representation of ENSO diversity appears to be model dependent and is often different in intensity, pattern and duration than observed (Cai et al., 2018). The different types of ENSO events have substantially different downstream impacts on the global climate and dynamics (Strnad et al., 2022).

The diversity of El Ni\~no events is commonly described by two distinct flavors, the Eastern Pacific (EP) and Central Pacific (CP) types. While the remote impacts, i.e. teleconnections, of EP and CP events have been studied for different regions individually, a global picture of their teleconnection patterns is still lacking. Here, we use Forman-Ricci curvature applied on climate networks constructed from 2-meter air temperature data to distinguish regional links from teleconnections. Our results confirm that teleconnection patterns are strongly influenced by the El Ni\~no type. EP events have primarily tropical teleconnections whereas CP events involve tropical-extratropical connections, particularly in the Pacific. Moreover, the central Pacific region does not have many teleconnections, even during CP events. It is mainly the eastern Pacific that mediates the remote influences for both El Ni\~no types.